We present a systematic study of the leading twist structure functions of the deuteron, F_2^D, b_{1,2}^D and g_1^D in a fully relativistic approach. Our study is based on a realistic Bethe-Salpeter amplitude for the deuteron, which is obtained as a solution to the homogeneous Bethe-Salpeter equation with a realistic NN kernel. Particular effort is made to connect the structure functions to the densities of the appropriate charges and currents. This allows for a systematic comparison between the relativistic and nonrelativistic calculations, by analysing the same densities in both approaches. Thus, the sources of the relativistic effects in the structure functions are understood and clearly distinguished from variations caused by the differences in the model parameters. We present both the formalism and extensive numerical calculations for all steps of our analysis. We find that the nonrelativistic and relativistic calculations are qualitatively very much alike. However, three main features systematically distinguish a consistent relativistic approach from the nonrelativistic one: (i) the binding effects are larger, (ii) the effect of Fermi motion at high $x$ is stronger and (iii) the relativistic description of the structure functions b_{1,2}^D is fully consistent, unlike the nonrelativistic approach, which is internally inconsistent and violates the fundamental sum rules.

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formalism II: Realistic $NN$-interaction does not yet have a rating.
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